In introductory statistics, what does it mean to say a statistic is resistant?

• A. It always equals the population parameter when the sample is random.
• B. It becomes larger as the sample size increases, regardless of the data values.
• C. It has a smaller standard deviation than any other statistic computed from the same data.
• D. It is not greatly affected by a small number of extreme values (outliers).

Answer: (D)

Verified step by step guidance

1. Understand that a statistic is a numerical summary computed from sample data, such as the mean, median, or standard deviation.
2. Recognize that some statistics are sensitive to extreme values (outliers), meaning their values can change significantly if outliers are present.
3. Learn that a resistant statistic is one that does not change much when a small number of extreme values are added or removed from the data set.
4. For example, the median is resistant because it depends on the middle value(s) of the ordered data and is less influenced by outliers, whereas the mean is not resistant because it is affected by all values including extremes.
5. Therefore, saying a statistic is resistant means it remains relatively stable and is not greatly affected by outliers or extreme data points.